Simplifying Expressions with Exponents for 13-Year-Old Students

Let's simplify each part step by step.

1. Simplify 64f^0:

Remember that any number or letter raised to the power of 0 is 1 (except when the base is zero). So:

f^0 = 1

Therefore:

64f^0 = 64 × 1 = 64

2. Simplify (16x^8)^{3/4}:

This means raising 16x^8 to the power 3/4. Let's break it into steps:

1. Write inside the parenthesis separately: 16 and x^8.
2. Apply the power to both: 16^{3/4} and (x^8)^{3/4}.
3. Simplify 16^{3/4}: - First find the 4th root of 16 because of the denominator 4. The 4th root of 16 is 2 (since 2^4 = 16). - Now raise that result to the power 3: 2^3 = 8.
4. Simplify (x^8)^{3/4}: - When raising a power to a power, multiply the exponents: 8 × (3/4) = 24/4 = 6. - So, (x^8)^{3/4} = x^6.

Putting it together:

(16x^8)^{3/4} = 8x^6

Final answers:

• 64f^0 = 64
• (16x^8)^{3/4} = 8x^6